Dynamical Analysis of an Age-Structured SVEIR Model with Imperfect Vaccine

Yanshu Wang and Hailiang Zhang ()
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Yanshu Wang: School of Information Engineering, Zhejiang Ocean University, Zhoushan 316022, China
Hailiang Zhang: School of Information Engineering, Zhejiang Ocean University, Zhoushan 316022, China

Mathematics, 2023, vol. 11, issue 16, 1-19

Abstract: Based on the spread of COVID-19, in the present paper, an imperfectly vaccinated SVEIR model for latent age is proposed. At first, the equilibrium points and the basic reproduction number of the model are calculated. Then, we discuss the asymptotic smoothness and uniform persistence of the semiflow generated by the solutions of the system and the existence of an attractor. Moreover, LaSalle’s invariance principle and Volterra type Lyapunov functions are used to prove the global asymptotic stability of both the disease-free equilibrium and the endemic equilibrium of the model. The conclusion is that if the basic reproduction number R ρ is less than one, the disease will gradually disappear. However, if the number is greater than one, the disease will become endemic and persist. In addition, numerical simulations are also carried out to verify the result. Finally, suggestions are made on the measures to control the ongoing transmission of COVID-19.

Keywords: SVEIR model; latent age; imperfect vaccine; Lyapunov functions; stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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